If cotA+cotB+cotC=3^1/2 the prove that the triangle is isosceles triangle.The question is related to properties of triangle lesson....]
This question is wrong. It should be an equilateral triangle. I will prove this for an equilateral triangle.
In an equilateral triangle `A=B=C` and `A+B+C = pi`
Therefore, `A=B=C= pi/3`
`cot(A)+cot(B)+cot(C) = cot(pi/3)+cot(pi/3)+cot(pi/3)`
Therefore if ABC is an equilateral triangle,
And vice versa.
this is for an equilateral triangle.
if its an equilateral triangle then A=B=C and also A+B+C=pi
3A (or 3B or 3C)=pi
=>A (or B or C)=pi/3
cotA +cotB +cotC=cot(pi/3)+cot(pi/3)+cot(pi/3)
hence it is an equilateral triangle